FLU
M
flu
with, an ordinary Charcoal Fire. See Antimony ; fee alfo
PotfNDER-Y-
FLUXION, in Medicine, a fudden Collection of mor- bid Matter in any Part of the Body.
fluxions arife either from the Weaknefs, Flaccidity, and Inactivity of the Part affected, which does not difperfe, pro- trude, or expell the Humors naturally receiv'd into it : Or ■from the Derivation of fame extraordinary Quantity of pec- cant Matter from fome other Part.
This latter is properly called Dcfuxion, and by the An- tients, Attraction. See Defluxion.
Fluxions are occafion'd by Motion* Heat, Pain, Fomen- tation, &c.
A Fluxion, or Defluxion on the Lungs, is called a Ca- tarrh. See Catarrh.
Fluxions, or the Method of Fluxions, is the Arithme- tic!:, or Analyfis, of infinitely fin all variable Quantities; or the Method of finding an Infinitesimal, or infinitely fmall Quantity, which being taken an infinite Number of times, becomes equal to a given Quantity. See Infinite, and Infinitesimal.
Sir J. Newton, and after him all the Engliffo Authors, call thefe infinitely Email Quantities, Fluxions 5 as confidering them as the momentary Increments or Decrements ofvariable Quantities, e.gr. of a Line confider'd as generated by the Flux of a Point 5 or of a Surface generated by the Flux of a Line.
Accordingly, the variable Quantities are called plenty or pacing gitantitics ; and the Method of finding either the Fluxion, o* the Fluent, the Method of Fluxions. See Method. M. Leibnitz, and the Foreigners after him,confider the fame infinitely fmall Quantities as the ^Differences, or 'Dif- ferential of two Quantities $ and call the Method of find- ing thofe Differences, the ^Differential Calculus. See Cal- culus different talis.
Each of thefe ways of cohfidering and denominating, has its Advantages 5 which the Retainers to this, or that Me- thod, ftrenuoufly affert.
Variable Quantities, i.e. fuch as in the Genefis of Fi- gures by local Motion are continually increasing and dimi- nishing, arc certainly very properly denominated Fluents : And as all Figures may be conceiv'd as fo generated ; the in- finitely fmall Increments, or Decrements of fuch Quantities are very naturally denominated Fluxions.
Befide this Difference in the Name, there is another in the Notation.
Sir 7. Newton expreffes the Fluxion of a Quantity, as x by a Dot placed over it, as * ; and Mr. Leibnitz expreffes his Differential of the fame x by prefixing a d as d x ; each of which Methods of Notation has likewife its Advantage. See ^Differential Calculus.
Setting afule thefe circumftances, the two Methods are the fame.
The Method of Fluxions is one of the greateft, moil fubtile and fublimcDifcoveries of this, or perhaps any other Age : It opens a new World to us, and extends our Knowledge, as it were, to Infinity. It carries us beyond the Bounds that fcem'd to have been prefcrib'd to the human Mind 5 at leaft infinitely beyond thofe to which the antient Geometry was confined.
The Hiftory of this important Difcovery, as frcfli as it is, is a little dark, and hnbroiled. Two of the greatelt Men of this Age, do both ot them claim the Invention, Sir I. Newton, and M. Leibnitz 5 and nothing can be more glorious for the Method it ffelfj than the Zeal wherewith the Partialis of cither fide have afferted the Title.
To give the Reader a juft View of this noble Difpute, and of the Pretentions of each Party, we mail lay before him the Origines of the Difcovery, and mark where each Claim commenced, and how it was fupported.
The fir II time the Method made its Appearance inpublick, was in 1 684 ; when M. Leibnitz gave the Rules thereof in the Lciffic Acts of that Year 5 but the Demonstrations he kept to himfclf. The two Brothers, the 'Bernoulli's, were prefently flruck with it; and found out the Demonitrations, tho 1 very difficult; and practifed the Calculus with lurpriz- ing Succefs.
Thh is all we hear of it, till the Year 1687 ; when Sir J. Newton's admirable ^Principia came forth, which is al- niofl: wholly founded on the fame Calculus.
The common Opinion at that time, was, that Sir Ifaae, and M. Leibnitz had each invented it about the fame time : And what confirm'd it, was, that neither of them made any mention of the other 5 and that, tho' they agreed in the Subftancc of the thing, yet they differed in their ways of conceiving; called it by different Names, and uled different Characters.
In effect, Mr. Leibnitz's Character, was fuppos'd by Foreigners to be fomewhat more comodious than that of Sir Ifaac Newton $ accordingly, the Method loon fpreading it lelf throughout Europe, M. Leibnitz's Character went with it ; by which means the Geometricians were infcnilbly
as the fole, or principal Iii-
accuftomed too look on hin ventor.
The two Great Authors themfelves, without any feerhirig Concern, or Difpute as to the Property of the Invention^ eh- joy'd the glorious Profpect of theProgreffes continually mak- ing under their Aufpices - y till the Year 1699 : when the Peace began to be difturb'd,
M. Fatio, in a Treatife of the Line of fwiftefl 2)efcenti having declared that he was oblig'd to own Sir 1. Newtoit as the firft Inventor of the Differential Calculus, and tho firlt by many Years 5 and that he left the World to judge, whether M. Leibnitz, the fecond Inventor, had taken any thing from him; This precife Distinction between firit and fecond Inventor 5 with the Sufpicion it infinuated j faifed a Controvcrfy between M. Leibnitz, fupported by the Editor^ of the Leipfic ABa j and xhcEnglijh Geometricians, who declared for Sir /. Newton.
Sir Ifaac himfelf never appear'd on the Scene : His Glo- ry was become that of the Nation; and his Adherents^ warm in the Caufe of their Country, needed him not to animate them.
Writings fucceeded each other but (lowly, on either fide ; probably on account of the Diflance of Places 5 but the Controverfy «rcw Hill hotter and hotter: Till at length it came to fuchrafs, that in the Year i7ii,M. Leibnitz com- plain'd to the Royal Society, that Dr. Kiel had accufed him of publishing the Method ot Fluxions invented by Sir /. Newton, under other Names, and Characters.
He infifted, that no body knew better than Sir Ifaac himfelf, that he had Stolen nothing from him : and required that Dr. Kiel mould publickly difavow the ill Construction which might be put on his Words.
The Society, here appeal'd to as Judge, appointed a Com- mittee to examine all the old Letters, Papers, gfyC. that had paffed among the feveral Mathematicians, relating to the Point: And after a flrict Examen of all the Evidences that could be procured, gave in their Report, " That it
- ' did not appear that M. Leibnitz knew any thing of the
(t differential Calculus before a Letter wrote him by Sir 1". " Newton, and fent to him at 'Paris, in the Year i6fi 5 '* wherein the Method of Fluxions was fufficiently ex- (t plain'd, to let a Man of his Sagacity into the whole Mat- " ter-;. and that Sir /. Newton had even invented his Me- " thod before the Year 1669, and of confequence fifteen " Years before M. Leibnitz- had given any thing on the " Subject in the Lciffic AcJs." And thence they concluded, that Dr. Kiel had not at all injured Mr. Leibnitz in what he had laid.
The Sdciety printed this Cenfure of theirs, together with all the Pieces and Materials relating thereto, under the Ti- tle of Commercium Epiftolicum, de Analyfi promota. Lon- don, 1 712.
The Book was carefully distributed through Europe,- to vindicate the Title of the Engliffo Nation to the Difco- very 5 for Sit Ifaac, as already hinted, never appear'd ink: Whether it were, that he truifed his Honour with his Com- patriots, who were zealous enough in the Caufe 5 or whe- ther it were, that he were even Superior to the Glory there- of.
M. Leibnitz and his Friends could not iTiew the fame In- difference : He was accus'd of a Theft - 7 and the whole Com- mercium Epiftolicum either expreffes it in Terms, or insi- nuates it.
Soon after the Publication thereof, a lobfe Sheet waff printed at 'Paris, in behalf of M. Leibnitz, then at Vienna. It is wrote with a world of Zeal and Spirit, and maintains boldly, that the Method of Fluxions had not preceded that of Differences • and even insinuates, that it might have arofe from it.
The Detail of the Proofs on each fide would be too long, and could not be underilood without a large Comment; which mull enter into the deepeft Geometry.
M. Liebnitz had begun to work upon a Coimrtcrciitm E- fiJtolicU7V, in opposition to that of the Royal Society 5 but he died before it was .compleated.
It mult be own'd, there are Strong Prefumptions in fa- vour pf'M. Leibnitz ; Prefumptions, we mean, that he \vas no Plagiary : For that Sir Ifaac Newton was the firit Inven- tor, is pair, all Difpute: His Glory is fecure: The reafon- ab!e Part, even among the Foreigners, allow it; and the Queftion is only, Whether M. Liebnitz took it from him.^ or fell upon the fame thing with him : For in his 'Theory of abjlraft Motions, which lie dedicated to the Royal Acade- my, in J671, before he had feen any thing of Sir Ifaac New- ton's, he already fuppofed infinitely fmall Quantities, fome greater than others 5 which is one of the great Principles of the System.
The Doftrine confifts of two Parts, viz. Fluxions pro- perly fo called, or the Diruct Method of Fluxions call'd alfo Calculus Tiiffcrentialis ; and the In-verfe Method of Fluxions, or Calculus Intcgralis*
The
